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Calculate unknown concentrations in acid-base titrations, determine pH at equivalence point, and generate approximate titration curves with step-by-step chemistry solutions.
Problem: 25.0 mL of 0.100 M HCl is titrated with 0.100 M NaOH. What is the concentration of NaOH at the equivalence point? What is the pH at equivalence?
Solution: At equivalence, moles of acid = moles of base.
n(HCl) = 0.100 M × 0.0250 L = 0.00250 mol
V(NaOH) = 0.00250 mol / 0.100 M = 25.0 mL
pH at equivalence for strong acid + strong base = 7.00 (neutral)
Problem: 25.0 mL of 0.100 M acetic acid (Kₐ = 1.8 × 10⁻⁵) is titrated with 0.100 M NaOH. Find the pH at the equivalence point.
Solution: At equivalence, all acid is converted to its conjugate base (CH₃COO⁻).
[CH₃COO⁻] = (0.100 × 25.0) / (25.0 + 25.0) = 0.0500 M
K_b = K_w / K_a = 1.0 × 10⁻¹⁴ / 1.8 × 10⁻⁵ = 5.56 × 10⁻¹⁰
[OH⁻] = √(K_b × [CH₃COO⁻]) = √(5.56 × 10⁻¹⁰ × 0.0500) = 5.27 × 10⁻⁶ M
pOH = -log(5.27 × 10⁻⁶) = 5.28, pH = 14 - 5.28 = 8.72
Problem: 25.0 mL of H₂SO₄ (diprotic acid) requires 30.5 mL of 0.150 M NaOH to reach equivalence. What is the concentration of H₂SO₄?
Solution: H₂SO₄ has 2 protons (nₐ = 2), NaOH has 1 hydroxide (n_b = 1).
C₁ × V₁ × nₐ = C₂ × V₂ × n_b
C₁ × 25.0 × 2 = 0.150 × 30.5 × 1
C₁ = (0.150 × 30.5) / (25.0 × 2) = 0.0915 M
Where C₁ and C₂ are concentrations, V₁ and V₂ are volumes, and nₐ and n_b are the number of protons/hydroxides donated per molecule.
For a strong acid + strong base titration, the equivalence point pH is 7.00. For weak acid + strong base, the pH at equivalence is > 7 (basic) due to conjugate base hydrolysis. For strong acid + weak base, the pH is < 7 (acidic).
Titration is a laboratory technique used to determine the concentration of an unknown solution (analyte) by reacting it with a known concentration solution (titrant). The point at which the reaction is complete is called the equivalence point.
The equivalence point is when the moles of acid equal the moles of base (theoretical). The endpoint is when an indicator changes color. A good indicator is chosen so the endpoint coincides closely with the equivalence point.
Acids like H₂SO₄ (sulfuric) or H₃PO₄ (phosphoric) donate more than one proton. The titration equation must account for the number of protons (nₐ) using C₁ × V₁ × nₐ = C₂ × V₂ × n_b.
Choose an indicator whose color change range includes the equivalence point pH. Phenolphthalein (8.3–10.0) works for strong/weak acid + strong base. Methyl orange (3.1–4.4) works for strong acid + weak base.
⚠️ Important Note: This calculator provides theoretical titration calculations assuming ideal solution behavior. Real-world results may vary due to temperature effects, activity coefficients, and experimental conditions. Always perform proper laboratory techniques and calibrations. This tool is for educational and reference purposes only — it does not replace professional laboratory analysis.